Makespan Reduction Research Articles

Development of scheduling methodology in a multi-machine flexible manufacturing system without tool delay employing flower pollination algorithm

This paper addresses machines, automated guided vehicles (AGVs), tool transporter (TT), and tools concurrent scheduling in a multi-machine flexible manufacturing system (FMS) for makespan minimization. The fewest number of copies of each tool type is employed to prevent tool delays, and job and tool shift times between machines are taken into account. The tools are placed in a central tool magazine (CTM), which shares and serves them to many machines to cut down the price of duplicating the tools in each machine. This simultaneous scheduling problem is challenging to solve because it entails determining the fewest tool copies of each tool kind without tool delay, assigning AGVs and tool copies to job-operations (jb-ons), ordering jb-ons on machines, and related trip operations such as deadheading and loaded flight times for both TT and AGVs. This paper uses a mixed-integer nonlinear programming (MINLP) framework to present the problem, and a flower pollination algorithm (FPA) is employed to solve it. For verification, a manufacturing company’s industrial problem is employed. The results show that employing two copies each for two tool types and one copy each for the remaining tool types causes no tool delay, reduction in makespan and cost, and the FPA outperforms the Jaya algorithm.

Mathematical model and simulated annealing algorithm for setup operator constrained flexible job shop scheduling problem

In the vast majority of the published article on flexible job shop scheduling problems (FJSP), machines are the only resources with limited capacities. There are also a sizable number of research articles in FJSP in which workers (machine operators) are constraining resources in addition to machines. In those articles, a worker performs the sequential steps of the production process and must stay with a machine. However, we argue that with the increasing adoption of numerically controlled machines with self-controlling capabilities, operators become machine tenders rather than individuals performing the sequential steps of the production process. Hence, the assumption of machine tenders as constraining resources that can result in the idling of expensive numerical controlled machines cannot be justified. Moreover, the replacement of machine tenders with automation and robotics increasingly becomes standard practice. In contrast, skilled setup operators remain critical and constraining resources since automating their tasks cannot be easily achieved. This paper proposed a mathematical model for a new setup operator constrained flexible job shop scheduling problem (SOC-FJSP) where setup operations are assumed to be anticipatory (detached). Contrary to a machine tender, a setup operator needs to stay with the machine only while performing setup. Once setup is completed, a setup operator becomes free and available to perform setup operations on a different machine. The assumption of a setup being detached from operations allows the overlapping of a setup operation of a job with the setup and processing of its preceding operation, enabling makespan reduction and better utilization of machine tools and setup operators. To solve the proposed mathematical model, we develop a simulated annealing (SA) algorithm. We further expand the model and the algorithm to account for sequence-dependent setup time and workload balancing among the setup operators. Extensive numerical studies were conducted to illustrate the various attributes of the proposed mathematical model and the convergence behavior of the proposed algorithm.

Multi-objective low-carbon hybrid flow shop scheduling via an improved teaching-learning-based optimization algorithm

In this article, for achieving an effective and environmental-friendly production scheduling, we investigate a multi-objective low-carbon hybrid flow shop scheduling problem (MLHFSP) with the consideration of machines with varied energy usage ratios. The problem is formulated by a multi-objective mathematical model with two optimization objectives, i.e., minimizing total carbon emission (TCE) and makespan (Cmax). We primarily analyse on the formation of TCE and derive its mathematical expression. MLHFSP is NP-hard, therefore, to tackle the model, an improved multi-objective teaching-learning-based optimization (ITLBO) algorithm is proposed. The ITLBO algorithm mainly contains global search based teaching phase and local search based learning phase. In ITLBO, a solution is represented by two vectors, i.e., job sequence vector and machine assignment vector. Sigma method is utilized to quantify each individual, and to avoid local optimum, sequential neighbourhood search (SNS) method is also adopted. Experimental results validate the feasibility and effectiveness of proposed ITLBO in addressing MLHFSP. The research findings help manufacturing engineers to seek a sophisticated balance between carbon emission reduction and makespan reduction.

Horus: Interference-Aware and Prediction-Based Scheduling in Deep Learning Systems

To accelerate the training of Deep Learning (DL) models, clusters of machines equipped with hardware accelerators such as GPUs are leveraged to reduce execution time. State-of-the-art resource managers are needed to increase GPU utilization and maximize throughput. While co-locating DL jobs on the same GPU has been shown to be effective, this can incur interference causing slowdown. In this article we propose Horus: an interference-aware and prediction-based resource manager for DL systems. Horus proactively predicts GPU utilization of heterogeneous DL jobs extrapolated from the DL model's computation graph features, removing the need for online profiling and isolated reserved GPUs. Through micro-benchmarks and job co-location combinations across heterogeneous GPU hardware, we identify GPU utilization as a general proxy metric to determine good placement decisions, in contrast to current approaches which reserve isolated GPUs to perform online profiling and directly measure GPU utilization for each unique submitted job. Our approach promotes high resource utilization and makespan reduction; via real-world experimentation and large-scale trace driven simulation, we demonstrate that Horus outperforms other DL resource managers by up to 61.5 percent for GPU resource utilization, 23.7-30.7 percent for makespan reduction and 68.3 percent in job wait time reduction.

Lot Streaming in Different Types of Production Processes: A PRISMA Systematic Review

At present, any industry that wanted to be considered a vanguard must be willing to improve itself, developing innovative techniques to generate a competitive advantage against its direct competitors. Hence, many methods are employed to optimize production processes, such as Lot Streaming, which consists of partitioning the productive lots into overlapping small batches to reduce the overall operating times known as Makespan, reducing the delivery time to the final customer. This work proposes carrying out a systematic review following the PRISMA methodology to the existing literature in indexed databases that demonstrates the application of Lot Streaming in the different production systems, giving the scientific community a strong consultation tool, useful to validate the different important elements in the definition of the Makespan reduction objectives and their applicability in the industry. Two hundred papers were identified on the subject of this study. After applying a group of eligibility criteria, 63 articles were analyzed, concluding that Lot Streaming can be applied in different types of industrial processes, always keeping the main objective of reducing Makespan, becoming an excellent improvement tool, thanks to the use of different optimization algorithms, attached to the reality of each industry.

Distribution slack allocation algorithm for energy aware task scheduling in cloud datacenters

Regarding the ever-increasing development of data and computational centers due to the contribution of high-performance computing systems in such sectors, energy consumption has always been of great importance due to CO2 emissions that can result in adverse effects on the environment. In recent years, the notions such as “energy” and also “Green Computing” have played crucial roles when scheduling parallel tasks in datacenters. The duplication and clustering strategies, as well as Dynamic Voltage and Frequency Scaling (DVFS) techniques, have focused on the reduction of the energy consumption and the optimization of the performance parameters. Concerning scheduling Directed Acyclic Graph (DAG) of a datacenter processors equipped with the technique of DVFS, this paper proposes an energy- and time-aware algorithm based on dual-phase scheduling, called EATSDCDD, to apply the combination of the strategies for duplication and clustering along with the distribution of slack-time among the tasks of a cluster. DVFS and control procedures in the proposed green system are mapped into Petri net-based models, which contribute to designing a multiple decision process. In the first phase, we use an intelligent combined approach of the duplication and clustering strategies to run the immediate tasks of DAG along with monitoring the throughput by concentrating on the reduction of makespan and the energy consumed in the processors. The main idea of the proposed algorithm involves the achievement of a maximum reduction in energy consumption in the second phase. To this end, the slack time was distributed among non-critical dependent tasks. Additionally, we cover the issues of negotiation between consumers and service providers at the rate of μ based on Green Service Level Agreement (GSLA) to achieve a higher saving of the energy. Eventually, a set of data established for conducting the examinations and also different parameters of the constructed random DAG are assessed to examine the efficiency of our proposed algorithm. The obtained results confirms that our algorithm outperforms compared the other algorithms considered in this study.

A Comparative Analysis of Heuristic Metaheuristic and Exact Approach to Minimize Make Span of Permutation Flow Shop Scheduling

The study of permutation flow shop scheduling issues has proved fascinating. Make span reduction has been explored extensively throughout the years as one of the many factors. If there are more than two machines, finding a schedule that optimizes total completion times for Permutation Flow Shop issues is NP Hard. The well-known Nawaz–Enscore–Ham (NEH) heuristic is acknowledged as the top performing approach for the permutation flow shop scheduling issue till now, according to the make span minimization criteria. For large-scale problems, however, the NEH approach takes a long time to discover an estimated optimum solution. Many researchers have offered heuristics and meta-heuristics as the time it takes to compute grows exponentially in proportion to the size of the problem. For the permutation flow shop scheduling problem, we proposed a genetic algorithm with the criterion of minimizing make span as the criteria. The method's performance is compared to that of the well-known NEH algorithm. Computational experiments on benchmark data sets revealed that the proposed approach produces satisfactory solutions in short computational cycles. Furthermore, it just requires a few user-defined parameters, making it relevant to real-world flow shop scheduling challenges. The findings reveal that, when compared to an exact technique, the proposed genetic algorithm (GA) is capable of rapidly seeking optimal solutions for most small-sized instances. Furthermore, the proposed GA continues to function satisfactorily for medium and large-scale instances and generates solutions in a reasonable period.

Optimizing makespan and resource utilization for multi-DNN training in GPU cluster

Deep neural network (DNN) has been widely applied in many fields of artificial intelligence (AI), gaining great popularity both in industry and academia. Increasing the size of DNN models does dramatically improve the learning accuracy. However, training large-scale DNN models on a single GPU takes unacceptable waiting time. In order to speed up the training process, many distributed deep learning (DL) systems and frameworks have been published and designed for parallel DNN training with multiple GPUs. However, most of the existing studies concentrate only on improving the training speed of a single DNN model under centralized or decentralized systems with synchronous or asynchronous approaches. Few works consider the issue of multi-DNN training on the GPU cluster, which is the joint optimization problem of job scheduling and resource allocation. This paper proposes an optimizing makespan and resource utilization (OMRU) approach to minimize job completion time and improve resource utilization for multi-DNN training in a GPU cluster. Specifically, we first collect the training speed/time data of all DNN models by running a job for one epoch on a different number of GPUs. The OMRU algorithm, integrating job scheduling, resource allocation, and GPU reuse strategies, is then devised to minimize the total job completion time (also called makespan) and improve GPU cluster resource utilization. The linear scaling rule (LSR) is adopted for adjusting the learning rate when a DNN model is trained on multiple GPUs with large minibatch size, which can guarantee model accuracy without the other hyper-parameters tune-up. We implement the OMRU algorithm on the Pytorch with Ring-Allreduce communication architecture and a GPU cluster with 8 nodes, each of which has 4 NVIDIA V100 GPUs. Experimental results on image classification and action recognition show that OMRU achieves a makespan reduction of up to 30% compared to the baseline scheduling algorithms and reach an average of 98.4% and 99.2% resource utilization on image classification and action recognition, respectively, with the state-of-the-art model accuracy.

H3CSA: A makespan aware task scheduling technique for cloud environments

AbstractTask scheduling is essential to enhance the performance of large scale collaborative and distributed e‐business and e‐science applications. A typical such application comprises multiple communicating tasks to be executed on virtualized resources also called as virtual machines (VMs). However, scheduling multiple tasks to VMs is non‐trivial and is proven to be NP‐Complete. The primary agenda of any scheduling technique is to reduce the makespan, which reflects the completion time of the exit task. Focusing on makespan reduction for scheduling multiple tasks across heterogeneous VMs, in this paper, we propose a model called H3CSA based on a meta‐heuristic crow search algorithm (CSA). In order to assess the performance of H3CSA, its performance is compared with baselines such as HEFT‐B, HEFT‐T, HEFT‐L, a genetic algorithm based technique (N‐GA) and particle swarm optimization based technique (PPSO). Simulation results show improved performance of H3CSA with respect to N‐GA and PPSO for smaller applications. However, considering sizeable applications H3CSA shows comparable performance with respect to N‐GA and improved results for PPSO.

Exploiting Machine Learning For Improving In-Memory Execution of Data-Intensive Workflows on Parallel Machines

Workflows are largely used to orchestrate complex sets of operations required to handle and process huge amounts of data. Parallel processing is often vital to reduce execution time when complex data-intensive workflows must be run efficiently, and at the same time, in-memory processing can bring important benefits to accelerate execution. However, optimization techniques are necessary to fully exploit in-memory processing, avoiding performance drops due to memory saturation events. This paper proposed a novel solution, called the Intelligent In-memory Workflow Manager (IIWM), for optimizing the in-memory execution of data-intensive workflows on parallel machines. IIWM is based on two complementary strategies: (1) a machine learning strategy for predicting the memory occupancy and execution time of workflow tasks; (2) a scheduling strategy that allocates tasks to a computing node, taking into account the (predicted) memory occupancy and execution time of each task and the memory available on that node. The effectiveness of the machine learning-based predictor and the scheduling strategy were demonstrated experimentally using as a testbed, Spark, a high-performance Big Data processing framework that exploits in-memory computing to speed up the execution of large-scale applications. In particular, two synthetic workflows were prepared for testing the robustness of the IIWM in scenarios characterized by a high level of parallelism and a limited amount of memory reserved for execution. Furthermore, a real data analysis workflow was used as a case study, for better assessing the benefits of the proposed approach. Thanks to high accuracy in predicting resources used at runtime, the IIWM was able to avoid disk writes caused by memory saturation, outperforming a traditional strategy in which only dependencies among tasks are taken into account. Specifically, the IIWM achieved up to a 31% and a 40% reduction of makespan and a performance improvement up to 1.45× and 1.66× on the synthetic workflows and the real case study, respectively.

Stochastic resource-constrained project scheduling problem with time varying weather conditions and an improved estimation of distribution algorithm

Construction projects with outdoor operations are affected by time-varying weather conditions. However, most existing research on stochastic resource-constrained project scheduling problems (SRCPSPs) considers activity duration as a random variable from a time-independent distribution. To address this issue, this study investigates SRCPSP under time-varying weather conditions; an improved estimation of distribution algorithm (EDA) including a ranking and selection method using common random numbers is proposed for enhancing the performance of project scheduling. The benchmark J120 dataset from PSPLIB and a practical case of windfarm construction are used to validate the improved EDA. For three randomly selected cases from the J120 dataset, the improved EDA can reduce the expected makespan by 17.0, 29.4, and 12.5 days when compared with deterministic scheduling. The corresponding makespan reductions obtained by the original EDA are 10.8, 22.7, and 7.1 days. Similarly, the improved EDA obtains 23% higher expected makespan reduction for the practical case.

Simulation and modelling of hybrid heuristics distribution algorithm on flow shop scheduling problem to optimize makespan in an Indian manufacturing industry

This study presents a heuristic formulation of the flow shop scheduling problem by the hybrid algorithm fitness function. The genetic algorithm is used to model the time-estimates such as makespan and completion time. This paper aims to optimize the sequence-independent and sequence-dependent time-estimates. The production scheduling parameters such as permutation, non-permutation, no-wait, tardiness, and several workstations are identified from a piston manufacturing industry, in Northern India. The MATLAB programming in heuristics algorithm distribution function resulted in reduction of makespan of the product by five times. The reduced completion time is 23 minutes for the piston ring product and 26 minutes in cumulative validation of the proposed model. The cumulative optimized standard error of 0.26; (n=3) simulate and synthesize the suggested model with its validation. The system efficiency through completion time optimization ranged from 70-82 percent in piston ring, and 63-89 percent in cumulative validation of the model has been worked out for each machine type. The data generated through system optimization helps the scientific world and entrepreneurs in advancement of sequence-based transportation.

Fuzzy Gilmore and Gomory algorithm: Application in robotic flow shops with the effects of job-dependent transportation and set-ups

This paper addresses the scheduling of robotic cells with job-dependent transportation and set-up effects with fuzzy methodology. Since transportation and set-up times are a large portion of the production time in a flexible manufacturing cell, ignoring these parameters may cause significant errors in determining the optimal makespan. Furthermore, determining the exact values of these time parameters is a challenging task. To overcome this problem, we represent these parameters using fuzzy L-R numbers. Using the capability of fuzzy numbers to represent approximate values, we can represent these parameters without losing valuable information. For generating the optimal part sequencing in the cells, the Gilmore and Gomory algorithm is modified, and instead, a fuzzy Gilmore and Gomory algorithm is developed. We compare the results of the proposed fuzzy method with those of crisp ones. The results indicate the superiority of the proposed algorithm in terms of robustness, flexibility, and reduction of makespan.

Pengembangan Model Optimasi Artificial Neural Network pada Penjadwalan Produksi Snack Tortilla

Production on May 2019, PT X produced 29,159 kg of Tortillas to be marketed domestically and abroad. The large amount of production shows the high consumer interest in Tortilla, which makes PT X produce large quantities in 1 month. Production of 29,159 kg was completed in 3 weeks with 3 shifts in 7 working days in the first and third week, and 6 working days in the second week. Inaccurate production planning makes Tortilla production exceed warehouse capacity, indicating that the production process is still running even though the number in June is as much as 17,346 kg and 26,835 kg in July resulting in overproduction of 6% in May 2019 and 15% in June 2019 so that there was an increase in July 2019 to 50%. The implementations of the Artificial Neural Network (ANN) method based on Particle Swarm Optimization (PSO) using the Steepest Ascent Hill Climbing Algorithm (SAHC) areoptimize the final mean flow time by 51%, reduction in makespan by 0.5 in MayJune and 0.1 in July, and a reduction in lateness by 13% after reprocessing results in an optimization that can overcome the problem of overproduction.

A dynamic load scheduling in IaaS cloud using binary JAYA algorithm

Datacenters receive dynamic workloads with disparate specifications to be scheduled on virtual machines (VMs). These unpredictable, alarmingly growing workloads with varying resource specifications may bring down the servers of datacenters into an imbalanced state. Thus, resulting in low resource utilization and high energy consumption among the servers. To cater to the need of fluctuating on-demand resource provisioning, it is essential to scale up the ability and capacityof existing infrastructure through virtualization. Moreover, due to the involvement of conflicting scheduling constraints, load scheduling in cloud computing fall under NP-hard problem. An effective scheduling mechanism in amalgamation with a load balancing strategy based on binary JAYA is implemented to alleviate the challenges as mentioned above. This technique not only improves resource utilization but also brings down the degree of energy consumption and makespan while keeping the whole system balanced. At first, it focuses on evoking a load balancing procedure to uniformly disperse the loads among VMs based on the compatibility between the tasks and VMs and secondly, JAYA algorithm is executed to find the best possible mapping of tasks onto VMs. In order to appraise the efficacy of the proposed algorithm, the scheduling of independent and non-preemptive tasks is simulated in CloudSim using a benchmark parallel workload by NASA-iPSC. Experiments are conducted in both homogenous and heterogeneous environments. The proposed algorithm is statistically validated using the Friedman test, followed by a Holm’s test. The proposed approach is compared over other algorithms such as Round Robin (RR), binary Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). The simulation results show a notable amelioration over other mentioned algorithms by an increase of resource utilization with 18.47% (GA), 12.65% (BPSO) and 4.18% (GA), 2.51% (BPSO) and a reduction of makespan by 6.47% (GA), 4.35% (BPSO) and 4.17% (GA), 2.20% (BPSO) with an increasing number of tasks and VMs in two different test cases respectively.

Improved co-scheduling of multi-layer printing path scanning for collaborative additive manufacturing

Additive manufacturing processes, especially those based on fused filament fabrication mechanism, have a low productivity. One solution to this problem is to adopt a collaborative additive manufacturing system that employs multiple printers/extruders working simultaneously to improve productivity by reducing the process makespan. However, very limited research is available to address the major challenges in the co-scheduling of printing path scanning for different extruders. Existing studies lack: (i) a consideration of the impact of sub-path partitions and simultaneous printing of multiple layers on the multi-extruder printing makespan; and (ii) efficient algorithms to deal with the multiple decision-making involved. This article develops an improved method by first breaking down printing paths on different printing layers into sub-paths and assigning these generated sub-paths to different extruders. A mathematical model is formulated for the co-scheduling problem, and a hybrid algorithm with sequential solution procedures integrating an evolutionary algorithm and a heuristic is customized to multiple decision-making in the co-scheduling for collaborative printing. The performance was compared with the most recent research, and the results demonstrated further makespan reduction when sub-path partition or the simultaneous printing of multiple layers is considered. This article discusses the impacts of process setups on makespan reduction, providing a quantitative tool for guiding process development.

Toolpath planning for multi-gantry additive manufacturing

Additive Manufacturing (AM), specifically Fused Filament Fabrication (FFF) is revolutionizing the production of many products. FFF is one of the most popular AM processes because it is inexpensive, requires little maintenance, and has high material utilization. Unfortunately, long cycle times are a significant drawback that prevents FFF from being more widely implemented, especially for large-scale components. In response to this, printers that employ multiple independent FFF printheads simultaneously working on the same part have been developed, and multi-gantry configurations are now commercially available; however, there is a dearth of formal research on multi-gantry path planning, and current practices do not maximize printhead utilization or as-built mechanical properties. This article proposes a novel methodology for generating collision-free toolpaths for multi-gantry printers that yields shorter print times and superior mechanical properties compared with the state of the art. In this, a metaheuristic approach is used to seek near-optimal segmentation and scheduling of each layer while a collision checking and resolution algorithm enforces kinematic constraints to ensure collision-free solutions. Simulation is used to show the resulting makespan reduction for various layers, and the proposed methodology is physically implemented and verified. Tensile testing on samples printed via the current and proposed methods confirm that the proposed methodology results in superior mechanical properties.

Makespan-minimization workflow scheduling for complex networks with social groups in edge computing

Abstract Edge computing enables users to offload certain computation loads in complex applications to a nearby network consisting of multiple mobile devices such that the mobile devices’ resources can be integrated to afford these complex applications. Due to the social relationships among the owners of mobile devices, networks in edge computing are always complex and consist of multiple sub-networks intersecting at several joint devices. In such complex networks, a joint device can communicate with all devices belonging to all sub-networks that intersect at this joint device while a general device can only communicate with the devices belonging to the same sub-network. This paper studies the makespan-minimization workflow scheduling problem for the aforementioned complex networks in edge computing environments, and formulates the problem as an integer program. Due to the limited energy capacity of each device, the dependence among workflow tasks, as well as network complexity, it is challenging to achieve feasible scheduling solutions for the concerned problem. Therefore, we propose a family of task allocation strategies to cope with different types of tasks in the workflow. These strategies are further integrated with a greedy strategy to construct an improved greedy search (IGS) algorithm which is capable of generating feasible solutions satisfying all constraints. In addition, we propose an improved composite heuristic (ICH) algorithm that employs IGS to initialize a feasible solution and uses a two-layer improvement scheme to further enhance the quality of the initial solution. Simulation results show that our proposed IGS achieves an 100% probability of generating feasible solutions, as compared to a 2.3% probability achieved by using the general round-robin scheduling algorithm. Furthermore, IGS and ICH outperform the counterpart scheduling algorithms in terms of makespan reduction.

OASM: An overload‐aware workload scheduling method for cloud computing based on biogeographical optimization

SummaryWith the daily increase in the number of cloud users and the volume of submitted workloads, load balancing (LB) over clouds followed by a reduction in users' response time is emerging as a vital issue. To successfully address the LB problem, we have optimized workload distribution among virtual machines (VMs). This approach consists of two parts: Firstly, a meta‐heuristic method based on biogeographical optimization for workload dispatching among VMs is introduced; secondly, we propose an innovative heuristic algorithm inspired by the “Banker algorithm” that runs in core scheduler to control and avoid VM overloads. The combination of these two (meta‐)heuristic algorithms constitutes an LB approach through which we have been able to reduce the value of the makespan to a reasonable time frame. Moreover, an information base repository (IBR) is introduced to maintain the online processing status of physical machines (PMs) and VMs. In our approach, data stored in IBR are retrieved when needed. This approach is compared with well‐known (non‐)evolutionary approaches, such as round‐robin, max‐min, MGGS, and TBSLB‐PSO. Experimental results reveal that our proposed approach outperforms its counterparts in a heterogeneous environment when the resources are smaller than the workloads. Moreover, the utilization of physical resources gradually increases. Therefore, optimal workload scheduling, as well as the lack of overload occurrence, results in a reduction in makespan.

Short-term production scheduling with non-triangular sequence-dependent setup times and shifting production bottlenecks

A novel mathematical model is introduced that allows solving real-life scheduling problems in complex multi-stage machine environment with (i) non-triangular sequence-dependent setup times and (ii) shifting production bottlenecks, both of which are important aspects appearing in varying manufacturing industries. The primary goal is to minimise the tardiness of customer orders, which may consist of multiple production orders each in turn composed of several batches. A secondary objective is to maximise the production capacity utilization as measured by the makespan. The model is elaborated for general animal-feed plants which have to deal with the particular production scheduling problem on a daily basis. Dispatching rules are introduced to enhance the optimization progress. Numerical experiments show that optimising the model leads to schedules that meet the due dates. Moreover, by reducing the mean idle time of production lines with 35.6%, the optimization leads to a makespan reduction of 6.5% on average compared to real-life applied schedules.